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# Other Index 6: Higher geometry of fields and matrix theory

Other Index | 1: Natural Selection | 2: Society | 3: Multistable System | 4: DAMS | 4½: DAMS II | 5: Epistemology | 6: Higher geometry of fields and matrix theory | 7: Psychiatric Applications | 8: Conditioned Reflex | 9: Oddments | 10: Unsolved Problems | 11: Quotations | 12: Subjective | 13: Personal Notes | 14: Slogans and Aphorisms

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1. Divider: 6
2. Section Title: Higher geometry of fields and matrix theory
3. Equation of the plane which contains n consecutive points of the path, 1829.
4. A path is fixed (in a given field) by any n combinations of t and x, 1425.
5. If some variables in a complete system are unobservable, a path fixed by n t,x combinations can be accertained empirically, by using substitute variables, 1413, numerical example 1470.
6. Knowledge of one form EXPRESSION for all values of 1...xºn;t is sufficient to define all the others. 5051.
7. Field cannot be transformed to show all the variables but one as part-functions 3764.
8. Numerical arrangement for maximal stability, 2529.
9. If, as matrices, EXPRESSION, then EXPRESSION, 1828.
10. Method for finding EXPRESSION [Lim xi, t?8], 2179.
11. Matrix representation with zero in main diagonal as premultiplier 2395.
12. Lists of numerical matrices suitable for sampling experiments: 5x5 { 2335 2336 2337 2338 2339 2340 2341 2342 2343 2344 2345 2346 2347 2348 2349 } , { 2402 2403 2404 2405 2406 2407 2408 2409 } , 4x4 { 2350 2351 2352 2353 2354 2355 2356 2357 2358 2359 } , { 2380 2381 2382 2383 2384 2385 2386 2387 2388 2389 } , 3x3 { 2368 2369 2370 2371 2372 2373 2374 2375 2376 2377 2378 } , 2x2 { 2362 2363 2364 2365 2366 }
13. M=MATRIX If latent roots of M equal none of those of A, neither B nor C can be wholly zero, 2655.
14. Determinant and latent roots of a matrix formed by adding a diagonal and a 'permutation' matrix, 3429, applied 3433.
15. If EQUATION, with roots r1,...,rn, to find ?rp/?aSt, 0750, 1824. i.e. effect of coefficient on a root. Example 2066, 2401.
16. The latent roots are invariant when variables are replaced by derivatives. 3717, 3719.
17. An electromechanical analogy (spring and mass / condenser etc) in detail 4998.
18. Test for stability by dominant root, 2072.
19. Finding latent roots by Mallock machine, 2179.
20. Forming system with given roots 1818, 2444.
21. Test for stability of EQUATION [x'=Ax] by complex variable theory, 2030. An example 2267.
22. If one variable is made more self-stable, the whole may become unstable, 2423, 2454, 2463, 2458, 2460.
23. If a number, positive or negative, is added to all non-diagonal elements, the system becomes unstable when the number is large enough, 2772.
24. Characteristic equation of MATRIX 2780.
25. If A dominates B, the latent roots of the whole are just those of A and those of B, 2678.
26. If ajk=ajk + ibjk, and [ajk] has roots ?1...?n, then MATRIX has roots ?1...?n , ?1* ... ?n* 3917.
27. Nearly-decomposible matrices. Reprint 125.
28. Transforming a matrix to reduced form 5297.
29. Graphs and asymptotic forms of finite Boolean relation matrices and stochastic matrices. Reprint 193.
30. (Mod 12) MATRIX has VECTOR as equilibrium (and 23 other, given, vectors), 6163.
Other Index | 1: Natural Selection | 2: Society | 3: Multistable System | 4: DAMS | 4½: DAMS II | 5: Epistemology | 6: Higher geometry of fields and matrix theory | 7: Psychiatric Applications | 8: Conditioned Reflex | 9: Oddments | 10: Unsolved Problems | 11: Quotations | 12: Subjective | 13: Personal Notes | 14: Slogans and Aphorisms

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